Archive for March, 2017

Diolch yn fawr, thank you very much. As can be seen from your previous work (attached), neither Edward Evans nor Elizabeth Gunter were baptized in St. Mary’s Cusop, and it was your opinion that they were baptized in a nearby church. I have done some more research since then and found Welshjournals.llgc.org.uk. I found that William Davies of TreGunter came from Llanigon, where the Watkins family, of which he was one, had very close links with the Llanigon Family of Gunter. As can be seen from the attached direct line, Edward Evans IV was baptized in Llanigon, which is close to Cusop. I am not sure whether Llanigon is in Hereford or Powys. So St Eigon, Llanigon may have baptismal records. I know that St. Michael’s Cleirwy or Clyro is in Powys, so is the church in Hay (Y Gelli Gandryll). I also found that the Gunter family have or had had connections wth Llanigon since the eleventh century. So this will be fine. Gunter is a Norse name as the above journal confirms, so any Gunter or Havard or Aubrey will have an ancient lineage, easily verifiable by Norse or continental DNA. The name Evans is of course ap Ifan, and would have been in that area to time immemorial. The intermarried with the Princes so any family member will have a lineage back to the Princes.

Cyfarchion,

Myron Evans

In a message dated 31/03/2017 15:51:22 GMT Daylight Time, writes:

Dear Mr Evans,

Thank you for your email of 29 March. Before I pass your enquiry to the research service I just want to make sure that we will be on the right lines. You would like us to search for the baptism of Edward Evans and Elizabeth Gunter in the period 1710 – 175 in the registers of Cusop and Clifford (the records of Glasbury should be with Powys Archives). If that is correct, I would suggest we start with those parishes then if no relevant baptisms are found report back to you before extending the search outwards. Could you confirm whether you would like to proceed on that basis?

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There was the usual intense international interest from the best universities, institutes and similar. There have been consultations to 29/3/17 in March from nineteen out of the world’s top twenty universities by Webometrics, Times, QS and Shanghai rankings: Berkeley, Columbia, Texas A and M, U Penn, UCLA, Texas Austin, Wisconsin Madison*, Yale*, Michigan, EPF Lausanne, ETH Zurich, Edinburgh, Oxford, Imperial, Toronto, Stanford, Cambridge, NU Singapore and University College London.

Sir William Rowan Hamilton is known as Rowan Hamilton in Trinity College Dublin, of which I am sometime Visiting Academic. He was appointed to the Civil List on April 27th 1844 with a pension of £200 a year (about £22,319 a year today). My Civil List Pension is £2,400 a year, so it has been eroded a lot in value since 1844. It is now an honorarium rather than a salary to live on. The Civil List Pension is akin to Order of Merit. Hamilton was appointed Professor of Astronomy in Dublin at the age of twenty two and was considered to be one of the best mathematicians in the world at the age of 18. His papers “On a General Method of Dynamics” (1834 and 1835) gave the Hamilton Principle of Least Action and also what are known now as the Euler Lagrange equations. These were actually discovered by Hamilton using the Euler principle of 1744 and using some of Lagrange’s ideas of 1760. He also inferred the Hamilton or canonical equations, defined the lagrangian and inferred the hamiltonian, the basis of quantum mechanics. In UFT176, (www.aias.us and www.upitec.org) the Quantum Hamilton Equations are inferred, in what has become a classic paper. The Hamilton Principle of Least Action can be used in many branches of physics and mathematics.

This is an important remark, precession is still present. These will be very interesting as usual, there are many possible advances that can be made by using the equations of fluid dynamics in orbital theory: the continuity equation (conservation of matter); Navier Stokes equation; conservation of energy equation and vorticity equation. All of these add new equations to the set of simultaneous differential equations. I will write new notes on this theme.

Many thanks for these clarifications, I fully agree that fluid dynamic effects must be handled like a potential (i.e. as given properties) for the Lagrange mechanism. Using the correct momentum (28) will not give qualitative changes in the numerical solution because I used a constant spin connection, only the numbers will change.
Eqs. 43-44 c an be solved for any assumed radial function R_r(r). Eq. 45 does not enter the calculation, it would be interesting to see if the angular momentum is really conserved for non-constant functions R_r.

Horst

Am 29.03.2017 um 10:42 schrieb EMyrone:

These are interesting comments. This note is based entirely on standard equations of the Lagrange and Hamilton dynamics applied to vectors, notably Eq. (3), which gives the correct momentum p from the Lagrangian (2), these are all contained in Marion and Thornton. The vector Euler Lagrange equation is Eq. (11), and leads correctly to the well known equations (20) and (21), the Leibniz equation and the equation of constraint (21). The kinetic energy is p dot p / (2m). The primary purpose of the note is to show that the correct momentum must be defined by p bold = partial lagrangian / partial r dot bold (see for example Marion and Thornton). Eqs. (22) – (24) work correctly for classical dynamics, but no longer work correctly for fluid dynamics. The correct momentum of fluid dynamics must be calculated from eq. (3) using the lagrangian (35). The correct momentum is p bold = m v bold, where v bold is given by Eq. (26). This is the same as the momentum used in UFT363, and leads to Eqs. (33) and (34). The spin connection partial R sub r / partial r must be regarded in the same way as the potential energy U(r). Neither is a Lagrange variable. The key point is that the momentum p bold can be obtained correctly from the lagrangian (2) if and only if Eq. (3) is used. This is checked from the fact that p bold is r bold dot in Eq.(2). Then use the rules of differentiation with r dot bold. For classical dynamics, Eqns (22) to (24) happen to work fortuitously, and these are of course the equations used by Marion and Thornton in their chapter seven. However, for fluid dynamics they no longer work, because the complete momentum is now:

p bold = x r dot e sub r bold + r theta dot e sub theta bold

where
x = (1 + partial R sub r / partial r)

Using this in Eqs. (2) and (3) gives the correct momentum from the correct lagrangian, containing the correct kinetic energy. The correct momentum is Eq. (28) multiplied by m. When used in Eq. (29) it leads to to Eqs. (33) and (34). Eq. (33) is different from that found in UFT363, because in UFT363, the correct factor x in Eq. (33) turned out to be x squared, as in Eq. (39) of this note. Therefore the lagrangian (35) cannot be used with Eq. (38). This result is by no means obvious. It shows that there is a certain amount of subjectivity in the Lagrange method as is well known. It is by no means obvious how to choose the Lagrange variables, and the choice of lagrangian is also subjective to some degree. These things emerge in for example quantum field theory. Fortunately the answer is simple, use Eq. (13), in which there is only one Lagrange variable, vector r bold. This leads to Eqs. (33) and (34). I suggest putting Eqs. (43) to (45) through Maxima to see how the orbital precession behaves. I do not think that the replacement of x sqaured of UFT363 by the correct x of this note will make any qualitative difference to the precession that you have already inferred numerically. It might affect the details of the precession, but the precession will remain.

It is difficult for me to understand this note for principal reasons. My interpretation is the following:

The Lagrangian method is based on the kinetic energy and generalized coordinates. The Euler-Lagrange equations are based on the kinetic energy of the generalized coordinates. These coordinates are found by coordinate transformations. In our case the radial coordinate is transformed by

r –> r + R_r(r)

where R_r(r) is a “distortion” of radial motion of a particle inferred by fluid dynamics. For the Lagrange mechanism this function has to be known a priori, it cannot result from the Euler-Lagrange equations. If we assume that the R_r function is to be determined dynamically by the dynamics, we need an additional equation of motion or state or whatever. In Lagrange theory, energy conservation is fulfilled. This is not necessarily the case if a “free floating” function is introduced. I guess that you had this in mind when saying that a Hamiltonian formulation is needed in addition to the Lagrangian formulation to determined the dynamics consistently.

So the question is where to take the conditions for R_r that must appear as a constraint in the Lagrange mechanism. The generalized coordinates should be r and theta, but what is the kinetic energy? Let’s assmume that the velocity, eqs.(26,27) of the note, is that derived from the coordinate transformation. Then the Euler-Lagrange equations (33,34) are correct, although they contain an unspecified function R_r (which is not time dependent).

I do not understand the part of the note after eqs.(33,34). Why do you introduce the Lagrangian (35)? Obviously this belongs to a different problem to be solved. And why should it be re-expressed to (36)? The momentum in Lagrange theory is a generalized momentum and needs not have the form (37).

On page 6 of the manuscript I cannot decipher the sentence “It is not possible to choose … as Lagrange varibles”. Which variables do you mean?
Eqs. (44) and (45) are derived from the same Euler-Lagrange equation and are not independent. It is true that (45) is a constant of motion but this is not suited for solving the equations because it is only of first order. What about using

H = 1/2 m v^2 + U(r) = const.

instead? Then we can determine partial R_r/partial r , and replace it in (43,44) so that we have only derivatives of time and the equation system could be solved by Maxima for example. In general, combination of Lagrange theory (which is for mass points primarily) and fluid dynamics (which is for distributed fields) may be a bit tricky.

Sorry for having written such a long sermon today.
Horst

Am 28.03.2017 um 10:44 schrieb EMyrone:

This note shows that the complete Lagrangian and Hamiltonian formulations are needed to describe fluid dynamics self consistently. When this is done UFT363 is slighly corrected to Eqs. (43) to (45), which can be solved simultaneously using Maxima to give the orbit and spin connection.

Posted in asott2 | Comments Off on Computations of 374(2) and 374(3): Precession Confirmed

This interest can be seen on the daily reports for today and yesterday. These can be based on the replicated and patented Osami Ide circuit (UFT311, UFT321 UFT364, Self Charging Inverter), which will bring in the second industrial revolution described by AIAS Fellow Dr. Steve Bannister in his Ph. D. Thesis on www.aias.us (Department of Economics, University of Utah). See also www.et3m.net and www.upitec.org. The Alex Hill company has recently signed a joint venture agreement with a company in the United States. I think that investment managers should be interested in this new industry. It should return a spectacular amount on investment. ECE theory describes the Osamu Ide circuit with precision (UFT311), whereas the obsolete standard model fails completely. See also the pulsed LENR report by AIAS Director Douglas Lindstrom on www.aias.us and his Idaho lecture. He is currently on a business trip to China, where there has been intense interest in ECE theory for some years. There are potentially huge new markets for spacetime devices all over the world. They could be used to power domestic appliances of the type manufactured by Bosch. They could also be made into power stations, large power plants, power devices for electric vehicles, power plants for ships and also aircraft and spacecraft, and should make the chemical battery industry obsolete. That is why Prof. Bannister describes them as powering the second industrial revolution. Wind turbines are already obsolete as well as completely useless. Governments should implement energy from spacetime devices as quickly as they can. They can also be distributed to the starving poor of many countries.

The effective wind speed in the Betws area now is now zero, 9 mph average wind speed minus 9 mph needed to start the turbines. So they are producing nothing at all at the cost of millions and complete ecological destruction. Mynydd y Gwair will also be completely useless. There will be less wind speed on Mynydd y Gwair than on Betws. The year round contribution of wind to demand in Wales is only about 2%. So all wind turbines in Wales should be demolished at developer expense, and all supply pylons and roads. All subsidies should be paid back by the developers. Solar is now 0.38%, and the solar panels in Mawr are useless. Often, solar is 0.00%, and never greater than about 0.8%. Nuclear is flat out, gas is almost flat out. Coal is about half capacity. Hydro is a pathetic 2.71%. This fiasco is the result of cabals forcing through their ideas on weak governments.

In the first instance, Eqs. (27) to (29) can be solved numerically using Maxima to check that the method gives the correct orbit (18). Then the algorithm can be modified to solve Eqs. (37), (38) and (40) numerically using a model for the function x defined in Eq. (31). Finally Eq. (44) can be added if the fluid is assumed to be incompressible, so both the orbit and x can be found. The caveat of this note explains why the note slightly corrects the equations of UFT363. The lagrangian method of UFT363 gives Eq. (47), which is different from the correct Eq. (37). The reason is that the kinetic energy of fluid gravitation, Eq. (48), is not in the required format (49) demanded by the Hamilton Principle of Least Action. The kinetic energy must be T(r bold dot, r bold). Sometimes it is simpler and clearer to derive results without the Lagrange method using both the Lagrange and Hamilton or canonical equations of motion.

The fundamental reason for the last note is that the Hamilton Principle of Least Action, from which is follows that the lagrangian must be defined as T(r bold dot) – U(r bold). I will explain this in another note to be distributed shortly. This method holds for any r bold dot. The method used in UFT363 did not satisfy the fundamental criterion for a lagrangian, which is why it did not lead to the correct momentum. The new method of UFT374 corrects this and leads to soluble sets of simultaneous partial differential equations. The new advance is that these can be tied in with the equations of hydrodynamics in many interesting ways. For background reading I suggest Marion and Thornton chapter five. So UFT374 will develop in this way. I recommend Marion and Thornton as far as it goes. It is now known that its section on the Einstein theory is wildly wrong. This was again shown by Horst’s numerical methods combined with analytical methods. Marion and Thornton is not easy, but is recommended reading. I remember doing lagrangian theory in the second year mathematics course at UCW Aberystwyth. It is not easy, but sometimes useful. I have used it many times throughout my research career. Sometimes it is better to use other methods. The method of UFT374 uses all the available dynamics, Lagrangian and Hamiltonian. UFT176 on the discovery of the quantum Hamilton equations, is now a famous paper, a classic by any standards. There is a hugely successful combination of analytical and numerical techniques in each UFT paper, mainly by Horst Eckardt, Douglas Lindstrom and myself, and many contributions by other Fellows.